f '(t) =   Math   dt

     Mostly I am interested in number theory, calculating Pi and other constants, fractals, strange attractors and so on. Obviously my love for math and my love for programming go hand and hand. In this section you will find some of my work dealing with cryptography, fractals I've thought up, and the math behind calculating elusive constants.

Projects:

Methods of calculating PI
Last worked: 07/09/2005  Version: 1.0
Description: These are just some formulas I thought up and either wrote a program for or just worked out. Many of these where thought up because of my on going goal to derive a formula that I can use with my extFloat class to calculate Pi. I want the formula to be interative, be able to easily calculate more precision with out having to start over (stop, save, continue), I also want it to converge relatively quickly and be able to display Pi upto the correctly calculated digits in real time.

Images and Data: [ Diagrams, Methods and Proofs pg.1 ]  [ Diagrams, Methods and Proofs pg.2 ]

Fractal calculation of PI
Last worked: 04/20/2004  Version: 2.0
Description: The pictures are going to be more explanatory than I can be but here goes. Take a right triangle with the legs both equal to 1. Draw a bisector that is perpendicular to the hyptonuse by definition and draw a line from the top of the virtical leg to the bisector. Draw a bisector of the new triangle and connect that line to the top of the same original leg. As the bisector halfs the angle and becomes closer and closer to being virtical, the line connecting the virtical leg and the bisector becomes closer to being a slice of the original circle with r=1. You take the area of the new triangle and minus half of the area of the last triangle to account for the error. Because of semmetry you can times this error correction by 2^n (where n is the triangle number). Graphically this is imagined by connecting the bisector to the line to the right of the bisector, forming a identical second triangle. For each new triangle, you must make two new triangles from the bisector. Each time you create a new triangle you are acounting for some of the error (The area of the original triangle vs. the circle). Look at the images... trust me =P.

Note: This method does not use any trigonometric functions to calculate the area. Only basic compuation is needed. Because of this, I am able to use the formula below along with extFloat to compute Pi in real time!

Images and Data: [ Final Diagram and Equation ]  [ First Diagram and Equation ]  [ Theory ]

Square Fractal
Finished: 1/05/2004  Version: 1.0
Description: Not much to say here. I was bored and began to draw fractals I knew of when I came across this one. To my knowledge it's original and completely useless =P. Basically it is just a square and you form a new square using one of the diagonals as the new side for the new square. The picture looks pretty at least =P.

Images and Data: